Numerical Computation of Circumferential Waves in Cylindrical Curved Waveguides

2020 ◽  
Vol 17 (10) ◽  
pp. 2050001
Author(s):  
Zhirong Lin ◽  
Peng Yu ◽  
Haokun Xu
Keyword(s):  
Numerical Computation ◽  
Cross Section ◽  
Analytical Solutions ◽  
Present Method ◽  
Complex Field ◽  
Analytical Technique ◽  
Trial Wavefunction ◽  
The Waves ◽  
Variational Statement ◽  
Circumferential Waves

We present a complex field general variational statement to study the waves propagating in the circumferential directions of cylindrical curved waveguides. A semi-analytical technique that has been applied on straight waveguides in the literature is reformulated to adapt to the circumferential directions and used for constructing the trial wavefunction in complex field. The method requires the waveguide to be analyzed to be geometrically and physically uniform along its circumferential axis; however, its circumferential cross-section can be arbitrarily complex. The formulation is verified using various examples, which were examined previously by other numerical or analytical solutions. Different cases were studied and comparisons with those published are also performed show the utility and advantages of present method.

Uniform Horizontal Groundwater Flow against Dispersion in a Shallow Aquifer: Two Analytical Models

1992 ◽  
Vol 23 (1) ◽  
pp. 1-12
Author(s):  
Ram Raj Vinda ◽  
Raja Ram Yadava ◽  
Naveen Kumar
Keyword(s):  
Point Source ◽  
Groundwater Flow ◽  
Cross Section ◽  
Analytical Solutions ◽  
Concentration Distribution ◽  
Analytical Models ◽  
Shallow Aquifer ◽  
Horizontal Cross Section ◽  
Flow Components ◽  
Reactive Pollutant

Analytical solutions converging rapidly at large and small values of times have been obtained for two mathematical models which describe the concentration distribution of a non reactive pollutant from a point source against the flow in a horizontal cross-section of a finite saturated shallow aquifer possessing uniform horizontal groundwater flow. Zero concentration or the conditions in which the flux across the extreme boundaries are proportional to the respective flow components are applied. The effects of flow and dispersion on concentration distribution are also discussed.

scholarly journals A novel method for the analytical solution of fractional Zakharov–Kuznetsov equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Rasool Shah ◽  
Hassan Khan ◽  
Dumitru Baleanu ◽  
Poom Kumam ◽  
Muhammad Arif
Keyword(s):  
Present Method ◽  
Decomposition Method ◽  
Fractional Derivatives ◽  
Adomian Decomposition Method ◽  
Current Method ◽  
Analytical Technique ◽  
Suggested Technique ◽  
Adomian Decomposition ◽  
Novel Method ◽  
The Given

AbstractIn this article, an efficient analytical technique, called Laplace–Adomian decomposition method, is used to obtain the solution of fractional Zakharov– Kuznetsov equations. The fractional derivatives are described in terms of Caputo sense. The solution of the suggested technique is represented in a series form of Adomian components, which is convergent to the exact solution of the given problems. Furthermore, the results of the present method have shown close relations with the exact approaches of the investigated problems. Illustrative examples are discussed, showing the validity of the current method. The attractive and straightforward procedure of the present method suggests that this method can easily be extended for the solutions of other nonlinear fractional-order partial differential equations.

Surfing the waves of seed dispersal

2021 ◽  
Author(s):  
Guillermo Abramson
Keyword(s):  
Seed Dispersal ◽  
Analytical Solutions ◽  
Analytical Modeling ◽  
Rule Of Thumb ◽  
Approximate Analytical Solutions ◽  
Animal Feeding ◽  
The Waves ◽  
Collection Sites

In this paper, we analyze a model of an animal feeding on fruits and dispersing their seeds, which are later deposited and capable of germination. The deposition of seeds away from their collection sites produces a delay in the dynamics, whose analytical modeling complicates the description in a way that would delight Nitant. We have found approximate analytical solutions, as well as numerical ones, but here I will emphasize on a typical physicists rule of thumb argument.

scholarly journals Correction to: Analytical Solutions for Tunnels of Elliptical Cross-Section in Rheological Rock Accounting for Sequential Excavation

2020 ◽  
Vol 53 (6) ◽  
pp. 2685-2685
Author(s):  
H. N. Wang ◽  
S. Utili ◽  
M. J. Jiang ◽  
P. He
Keyword(s):  
Cross Section ◽  
Analytical Solutions ◽  
Elliptical Cross Section ◽  
Elliptical Cross ◽  
Rheological Rock

The article Analytical Solutions for Tunnels of Elliptical Cross-Section in Rheological Rock Accounting for Sequential Excavation, written by H. N. Wang, S. Utili, M. J. Jiang, P. He, was originally published.

Static Analysis of Curved Beams with Clamped-Clamped Ends under Thermo Load

2011 ◽  
Vol 117-119 ◽  
pp. 1543-1546
Author(s):  
Xiao Fei Li ◽  
Chun Yi Cui ◽  
De Hai Yu
Keyword(s):  
Thermal Expansion ◽  
Static Analysis ◽  
Cross Section ◽  
Analytical Solutions ◽  
Virtual Work ◽  
Curved Beams ◽  
Curved Bridges ◽  
Internal Forces ◽  
The Cross ◽  
Scientific Base

Based on the principle of thermal expansion and theory of virtual work, a class of equations for in-plane displacements at three freedom direction and internal forces in the cross-section of statically indeterminate curved beams under thermo load are derived explicitly. In the case of infinite limit of radius, these equations coincide with that of the straight beams. Compared with the results of FEM, the analytical solutions by the proposed formulae are accurate. The analytical solutions obtained in this paper would provide a scientific base for further study and design of the curved bridges.

Experimental Investigation of Fatigue Performance of a 300 mm2 Copper Power Conductor

2013 ◽  
Author(s):  
Fachri P. Nasution ◽  
Svein Sævik ◽  
Stig Berge
Keyword(s):  
Fatigue Strength ◽  
Cross Section ◽  
Fatigue Crack Initiation ◽  
Fatigue Performance ◽  
Power Cables ◽  
Floating Structure ◽  
Copper Conductor ◽  
Sea Bed ◽  
Full Cross Section ◽  
The Waves

Electrical power cables are used in conjunction with floating units for provision of energy to installations on the sea bed, power from land to the floater, or export of power from a wind turbine to land. Power cables that are linked to a floating unit are subjected to fatigue loading from the waves and due to the movement of the vessel in the waves. Fatigue strength needs to be verified for design. Fatigue performance of a 300 mm2 stranded copper conductor was investigated. The experimental work included fatigue tests of individual wires and full cross section conductors including unlubricated and lubricated conductors. Individual wires from different layers were tested in tension-tension mode with stress ratio R = 0.1. Full cross-section conductors were tested in cyclic reversed bending with constant tension at ends, simulating the loading at the top end of a conductor hanging off a floating structure through a bellmouth. The objective of this paper is experimental assessment of the fatigue strength of a 300 mm2 copper conductor and to investigation of the mechanisms of fatigue crack initiation and growth in individual wires. At the time of submission the test program was still in progress, and conclusions are tentative only. An updated paper with complete results will be published at a later stage.

Effect of an Internal Open Crack on Pipes Wave Propagation

2011 ◽  
Vol 488-489 ◽  
pp. 375-378
Author(s):  
Alessandro Marzani ◽  
Marco Miniaci ◽  
Erasmo Viola
Keyword(s):  
Cross Section ◽  
Guided Waves ◽  
Dispersion Curves ◽  
Internal Crack ◽  
Open Crack ◽  
Axially Symmetric ◽  
Pipe Length ◽  
Pipeline Inspection ◽  
Non Invasive ◽  
The Waves

Stress guided waves in the sonic and ultrasonic regime are acknowledged as a powerful too lto inspect pipes in a non-invasive manner.A key point of the inspection procedure is related to the dispersive behavior of guided waves, that for agiven pipe is defined by the so-called dispersion curves. Such behavior, is generally predicted bymeans ofanalytical formulations. However, when the geometry of the pipe cross-section is not axially symmetric,such as in the presence of an open internal crack running along the pipe length, analytical formulations fail. Here, the computation of the guided waves properties for such a scenario is addressed via a SemiAnalytical Finite Element (SAFE) formulation in which the open crack is modeled at the mesh level.Different crack depths are considered and their effect on the waves dispersion curves are highlighted.The results could be of interest in pipeline inspection and monitoring.

Derivatives and Parameter Designs of Arbitrary Cross-Section Inhomogenous Beams’ Modes

2013 ◽  
Author(s):  
J. W. Xing ◽  
G. T. Zheng
Keyword(s):  
Cantilever Beam ◽  
Cross Section ◽  
Analytical Solutions ◽  
Structural Parameters ◽  
Arbitrary Cross Section ◽  
Mode Shapes ◽  
Design Parameters ◽  
Structural Parameter ◽  
Highly Sensitive ◽  
Sensitivity Analysis Method

As highly sensitive to structural parameter variations, it is necessary to study relations between derivatives of displacement modes and structural design parameters. This paper proposes an integral technique for obtaining the analytical solutions of slope and curvature modes of arbitrary cross-section inhomogeneous cantilever beam. The method is validated by comparing the computation results of modal frequencies and shapes with both numerical and analytical solutions. Furthermore, based on the presented method, we have established explicit expressions for the structural parameters sensitivity of the slope/curvature mode shapes. An example of parameter design is also presented for a cantilever beam with the proposed sensitivity analysis method.

scholarly journals TM Electromagnetic Scattering from PEC Polygonal Cross-Section Cylinders: A New Analytical Approach for the Efficient Evaluation of Improper Integrals Involving Oscillating and Slowly Decaying Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Mario Lucido ◽  
Chiara Santomassimo ◽  
Fulvio Schettino ◽  
Marco Donald Migliore ◽  
Daniele Pinchera ◽  
...  
Keyword(s):  
Cross Section ◽  
Electromagnetic Scattering ◽  
Computation Time ◽  
Electric Field Integral Equation ◽  
Analytical Technique ◽  
Electrically Conducting ◽  
Acceleration Technique ◽  
Integral Equation Formulation ◽  
The Matrix ◽  
Improper Integrals

The analysis of the TM electromagnetic scattering from perfectly electrically conducting polygonal cross-section cylinders is successfully carried out by means of an electric field integral equation formulation in the spectral domain and the method of analytical preconditioning which leads to a matrix equation at which Fredholm’s theory can be applied. Hence, the convergence of the discretization scheme is guaranteed. Unfortunately, the matrix coefficients are improper integrals involving oscillating and, in the worst cases, slowly decaying functions. Moreover, the classical analytical asymptotic acceleration technique leads to faster decaying integrands without overcoming the most important problem of their oscillating nature. Thus, the computation time rapidly increases as higher is the accuracy required for the solution. The aim of this paper is to show a new analytical technique for the efficient evaluation of such kind of integrals even when high accuracy is required for the solution.

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